Method and system for adaptively compensating closed-loop front-wheel steering control

ABSTRACT

An active front-wheel vehicle steering control system that employs closed-loop control includes an adaptive compensation sub-system that compensates for changes in vehicle dynamic parameters. The control system includes a dynamic parameter estimation sub-system that provides an estimated front cornering compliance and rear cornering compliance based on a steering wheel angle signal, a vehicle lateral acceleration signal, a vehicle yaw rate signal and a vehicle speed signal. The closed-loop control includes active gain for each of vehicle yaw rate, yaw acceleration, side-slip and side-slip rate, all based on the vehicle speed and vehicle dynamic parameter changes for use in generating a steering angle control signal to the front wheels of the vehicle.

TECHNICAL FIELD

This invention relates generally to closed-loop control for active vehicle front-wheel steering and, more particularly, to closed-loop control for active front-wheel steering that employs vehicle parameter estimates to compensate for changes in vehicle parameters.

BACKGROUND OF THE INVENTION

It is known in the art to employ automatic front-wheel vehicle steering based on vehicle dynamic information during a vehicle turn, or yaw, to enhance the vehicle stability. Active wheel steering control of a vehicle can improve vehicle stability over a conventional vehicle having only steerable front wheels. Open-loop automatic front-wheel steering provides a certain amount of front-wheel steering assist depending on the amount of front-wheel steering provided by the vehicle operator.

In the event that the vehicle is not following the steering path commanded by the vehicle operator, the closed-loop front-wheel steering is known to provide automatic assist based on vehicle state feedback. For example, slippery road conditions may prevent the vehicle from turning in the desired direction because the wheels may slip along the road surface. Further, the vehicle's rear quarter may “fish-tail,” also providing a different turn angle than was intended. Closed-loop front-wheel steering assist systems sense and compare the actual vehicle yaw rate and the commanded yaw rate, and generate a gain signal that provides the steering assist by the front wheels if the vehicle yaw rate and the commanded yaw rate are not the same. In these types of active front-wheel steering control systems, the open-loop control is always active and the closed-loop control is only activated if a potential handling and stability problem is detected.

Vehicles are designed so that the vehicle handling response complies with certain design specifications. Vehicle dynamic parameters define the vehicle handling response, where nominal parameters define a nominal vehicle handling response. The vehicle dynamic parameters of understeer coefficient, front cornering compliance and rear cornering compliance are the most dominant dynamic vehicle parameters for determining the stability and dynamic handling behavior of a vehicle. The understeer coefficient defines the vehicle yaw rate or turning radius for a particular steering angle. The front cornering compliance and the rear cornering compliance define the distribution of the vehicle side-slip to the front and rear axles when the vehicle is turning. The cornering compliances include the ratio defined by the lateral slip angle and the lateral force of the wheels. These parameters vary according to different vehicle loading, tire pressure, tire wear, and vehicle-to-vehicle variations of suspension characteristics, etc.

The control gains for front-wheel steering control systems, including both open-loop and closed-loop control, are optimally determined based on “out-of-factory” vehicle dynamic parameters. During operation of the vehicle over its lifetime, however, the factory-tuned vehicle parameters change as a result of short-term vehicle variations, such as vehicle loading and tire pressure changes, and long-term variations, such as tire wear and vehicle suspension age. When the vehicle dynamic parameters change from their original settings, the original steering control gains are no longer optimal, resulting in a different vehicle handling feel and vehicle stability degradation.

U.S. patent application Ser. No. 10/863,956, titled Real-Time Vehicle Dynamics Estimation System, filed Jun. 9, 2004, assigned to the assignee of this application and herein incorporated by reference, discloses a system that determines vehicle parameter estimates as a vehicle ages. It would be desirable to use such estimated dynamic parameters in a closed-loop front-wheel active steering system to improve the closed-loop steering control gains as the vehicle ages and is subjected to different conditions. By modifying the closed-loop gain schedule in response to estimated vehicle dynamic parameters, the handling feel and directional stability of the original vehicle can be maintained over the lifetime of the vehicle.

SUMMARY OF THE INVENTION

In accordance with the teachings of the present invention, an active front-wheel vehicle steering control method and system is disclosed that employs closed-loop control that includes an adaptive compensation sub-system that compensates for changes in vehicle dynamic parameters. A dynamic parameter estimation sub-system provides an estimated front cornering compliance and rear cornering compliance based on a steering wheel angle signal, a vehicle lateral acceleration signal, a vehicle yaw rate signal and a vehicle speed signal. A closed-loop control sub-system includes active gain for each of vehicle yaw rate, yaw acceleration, side-slip and side-slip rate based on the vehicle speed and vehicle dynamic parameter changes for use in generating a control steering signal to the front wheel.

Additional advantages and features of the present invention will become apparent from the following description and appended claims, taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of a front-wheel steering control system employing estimated vehicle dynamic parameters, according to an embodiment of the present invention;

FIG. 2 is a schematic block diagram of the closed-loop yaw rate feedback adaptive compensation process of the present invention;

FIGS. 3(a)-6(a) are graphs with vehicle speed on the horizontal axis and gain on the vertical axis showing typical closed-loop gain sensitivity for yaw rate feedback, yaw acceleration feedback, side-slip feedback and side-slip rate feedback, respectively, for changes in the front cornering compliance; and

FIGS. 3(b)-6(b) are graphs with vehicle speed on the horizontal axis and gain on the vertical axis showing typical closed-loop gain sensitivity for yaw rate feedback, yaw acceleration feedback, side-slip feedback and side-slip rate feedback, respectively, for changes in the rear cornering compliance.

DETAILED DESCRIPTION OF THE INVENTION

The following discussion of the embodiments of the invention directed to an active front-wheel steering system employing compensation for changes in vehicle dynamic parameters is merely exemplary in nature, and is in no way intended to limit the invention or its applications or uses.

FIG. 1 is a plan view of a vehicle 10 including front wheels 12 and 14 and rear wheels 16 and 18. The front wheels 12 and 14 are steered by a vehicle steering wheel 20. A steering angle sensor 22 measures the steering angle of the steering wheel 20 and provides a steering wheel angle signal δ_(H). The vehicle 10 includes an active front-wheel steering control system 30 that generates a front-wheel steering control signal δ_(F) that is applied to a front-wheel steering actuator 32 to steer the front wheels 12 and 14, as will be discussed in detail below.

The control system 30 includes an open-loop control sub-system 34 that provides an open-loop steering control signal δ_(OL) and a closed-loop control sub-system 36 that provides a closed-loop steering control signal δ_(CL). The control system 30 also includes a real-time vehicle dynamics estimation sub-system 40 that estimates the front cornering compliance D_(F) and the rear cornering compliance D_(R). In one embodiment, the dynamics estimation sub-system 40 is a real-time vehicle dynamics estimation system known in the art that employs a vehicle parameter estimator, a vehicle condition detector and a rich steering input detector for generating an estimated vehicle understeer coefficient and front and rear cornering compliances in real time based on various vehicle signals upon detecting the vehicle operating in a linear region. Alternatively, other real-time vehicle dynamics estimation systems may also be applicable. The control system 30 also includes a vehicle speed sensor 42 that provides a vehicle speed signal V_(X) to all of the open-loop control sub-system 34, the closed-loop control sub-system 36 and the dynamics estimation sub-system 40. The open-loop control sub-system 34 and the parameter estimation sub-system 40 also receive the steering wheel angle signal δ_(H). The closed-loop control sub-system 36 and the dynamics estimation sub-system 40 both receive a vehicle yaw rate signal Ω and a vehicle lateral acceleration signal Ay from suitable yaw rate and lateral acceleration dynamic sensors 46.

The open-loop control sub-system 34 includes an open-loop look-up table process block 50 that provides an open-loop front-wheel steering angle signal δ_(OL) from a look-up table. The open-loop front-wheel steering angle δ_(OL) signal as provided by the process block 50 is well known in the art.

The closed-loop sub-system 36 includes a pre-processing block 90 that receives the various sensor signals discussed above. The pre-processing block 90 operates as a command interpreter, provides sensor signal pre-processing and conversion, and provides closed-loop entrance and exit criteria. The pre-processing block 90 provides output signals including the actual vehicle yaw rate signal Ω, a yaw rate command signal Ω_(c), a vehicle side-slip feedback signal Vy and the derivative of the side-slip feedback signal dVy/dt. The yaw rate signal Ω and the yaw rate command signal Ω_(c) are applied to an adder 94 to obtain a yaw rate error signal Ω_(e) that is the difference between the commanded vehicle yaw rate and the actual vehicle yaw rate. A closed-loop pre-processing block that performs these functions is known in the art, and a detailed discussion of its operation is not necessary for a proper understanding of the invention.

The entrance and exit criteria for the closed-loop front-wheel steering assist are based on the vehicle side-slip and yaw rate errors. If the vehicle side-slip and yaw rate errors are great enough, then the pre-processing block 90 will close a switch 92 so that the closed-loop front-wheel steering command signal δ_(CL) is used to help provide the front-wheel steering to properly steer the vehicle. Additionally, the entrance/exit signal is applied a switch 80 so that if the closed-loop signal δ_(CL) is being used to help provide the front-wheel steering, then the open-loop signal δ_(OL) is not used.

The closed-loop steering signal δ_(CL) is a summation of several feedback signals including yaw rate feedback (RP), yaw acceleration feedback (RD), side-slip feedback (SP) and side-slip rate feedback (SD). The yaw rate error signal δ_(e) is applied to a yaw rate feedback look-up table 96 and a yaw rate feedback adaptive compensation process block 98. The look-up table 96 provides a predetermined yaw rate feedback angle signal based on the nominal front cornering compliance and the rear cornering compliance and the vehicle speed of the vehicle 10 in response to the yaw rate error signal Ω_(e). Yaw rate feedback look-up tables for a closed-loop front-wheel steering assist system are known in the art. The yaw rate feedback adaptive compensation process block 98 receives the vehicle speed signal Vx and the change in the front and rear cornering compliances ΔD_(F) and ΔD_(R), and provides a corrected yaw rate feedback angle signal as the front and rear cornering compliances change as the vehicle ages. The original yaw rate feedback angle signal and the corrected yaw rate feedback angle signal are sent to an adder 100 where they are combined to provide an adapted yaw rate feedback angle signal δ_(RP). Equation (1) shows how the adapted yaw rate feedback angle signal δ_(RP) is calculated in one non-limiting embodiment. $\begin{matrix} {\delta_{RP} = {{{K_{RP}^{o}\left( V_{x} \right)} \cdot \left( {\Omega_{c} - \Omega} \right)} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{RP}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{RP}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{RP}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot \left( {\Omega_{c} - \Omega} \right)}}} & (1) \end{matrix}$ where,

Ω is the yaw rate;

Ω_(c) is the yaw rate command;

K⁰ _(RP)(V_(x)) is the nominal yaw rate feedback gain table as a function of vehicle speed;

ΔD_(F) is the change in the front cornering compliance;

ΔD_(R) is the change in the rear cornering compliance;

ΔT is the deviation in the open-loop gain; and ${{{{{\frac{\Delta\quad K_{RP}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{RP}}{\Delta\quad D_{F}}}}_{o},\frac{\Delta\quad K_{RP}}{\Delta\quad D_{R}}}}_{o}$ is the yaw rate P-gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.

FIG. 2 is a schematic block diagram of the yaw rate feedback adaptive compensation process block 98. As shown, the yaw rate error signal Ω_(e) is multiplied by the corrected yaw rate feedback signal, as determined in accordance with equation (1), and then sent to an adder 100 for adding to the nominal gain to obtain the adapted yaw rate feedback angle signal δ_(RP). A similar schematic block diagram applies to each of the other gains as well.

FIGS. 3(a) and 3(b) are graphs with vehicle speed on the horizontal axis and yaw rate feedback angle on the vertical axis showing examples of gain sensitivities corresponding to changes in the front cornering compliance and the rear cornering compliance, respectively.

The yaw rate error signal Ω_(e) is applied to a derivative process block 104 that generates a derivative of the error signal dΩ_(e)/dt. The derivative error signal dΩ_(e)/dt is applied to a yaw acceleration feedback look-up table 106 and a yaw acceleration feedback adaptive compensation process block 108. The look-up table 106 provides a predetermined yaw acceleration feedback angle signal based on the nominal front cornering compliance and the rear cornering compliance and the vehicle speed of the vehicle 10. Yaw acceleration feedback look-up tables for a closed loop front-wheel steering assist system are known in the art. The yaw acceleration feedback adaptive compensation process block 108 receives the vehicle speed signal Vx and the change in the front and rear cornering compliances ΔD_(F) and ΔD_(R), and provides a corrected yaw acceleration feedback angle signal as the front and rear cornering compliances change as the vehicle ages. The original yaw acceleration feedback angle signal and the corrected yaw acceleration feedback angle signal are applied to an adder 110 to provide an adapted yaw acceleration feedback angle signal δ_(RD). Equation (2) shows how the adapted yaw rate feedback angle signal δ_(RD) is calculated in one non-limiting embodiment. $\begin{matrix} {\delta_{RD} = {{{K_{RD}^{o}\left( V_{x} \right)} \cdot \left( {{\overset{.}{\Omega}}_{c} - \overset{.}{\Omega}} \right)} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{RD}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{RD}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{RD}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot \left( {{\overset{.}{\Omega}}_{c} - \overset{.}{\Omega}} \right)}}} & (2) \end{matrix}$ where,

K⁰ _(RD)(V_(x)) is the nominal yaw acceleration feedback gain table as a function of the vehicle speed; and ${{{{{\frac{\Delta\quad K_{RD}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{RD}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{RD}}{\Delta\quad D_{R}}}}_{o}$ is the yaw-rate D-gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.

FIGS. 4(a) and 4(b) are graphs with vehicle speed on the horizontal axis and yaw acceleration feedback angle on the vertical axis showing examples of gain sensitivities corresponding to changes in the front cornering compliance and the rear cornering compliance, respectively.

The vehicle side-slip signal Vy from the pre-processing block 90 is applied to an inverter 114 and the inverted side-slip signal is applied to a side-slip feedback look-up table 116 and a side-slip feedback adaptive compensation process block 118. The look-up table 116 provides a predetermined side-slip feedback angle signal for the original front and rear cornering compliances and the vehicle speed of the vehicle 10. Side-slip feedback look-up tables for a closed loop front-wheel steering assist system are known in the art. The side-slip feedback adaptive compensation process block 118 receives the vehicle speed signal Vx and the change in the front and rear cornering compliance signals, and provides a corrected side-slip feedback angle signal as the front and the rear corning compliances change as the vehicle ages. The original side-slip feedback angle signal and the corrected side-slip feedback angle signal are applied to an adder 120 to generate an adapted side-slip feedback angle signal δ_(SP). Equation (3) shows how the adapted side-slip feedback angle signal δ_(SP) is calculated in one non-limiting embodiment. $\begin{matrix} {\delta_{SP} = {{{K_{SP}^{o}\left( V_{x} \right)} \cdot V_{y}} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{SP}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{SP}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{SP}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot V_{y}}}} & (3) \end{matrix}$ where,

K⁰ _(SP)(V_(x)) is the nominal side-slip feedback gain table as a function of the vehicle speed; and ${{{{{\frac{\Delta\quad K_{SP}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{SP}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{SP}}{\Delta\quad D_{R}}}}_{o}$ is the side-slip gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.

FIGS. 5(a) and 5(b) are graphs with vehicle speed on the horizontal axis and side-slip feedback angle on the vertical axis showing examples of gain sensitivities corresponding to changes in the front cornering compliance and the rear cornering compliance, respectively.

The derivative of the vehicle side-slip signal dVy/dt is applied to an inverter 122, and the inverted side-slip derivative (commonly called side-slip rate) signal is applied to a side-slip rate feedback look-up table 124 and a side-slip rate feedback adaptive compensation process block 126. The look-up table 124 provides a predetermined side-slip rate feedback angle signal based on the nominal front cornering compliance and the rear cornering compliance and the vehicle speed of the vehicle 10. Side-slip rate feedback look-up tables for a closed loop front-wheel steering assist system are known in the art. The adaptive compensation process block 126 receives the vehicle speed signal Vx and the change in the front and rear cornering compliance signals, and provides a corrected side-slip rate feedback angle signal. The original side-slip rate feedback angle signal and the corrected side-slip rate feedback angle signal are applied to an adder 128 that generates an adapted side-slip rate feedback angle signal δ_(SD). Equation (4) shows how the adapted side-slip rate feedback angle signal δ_(SD) is calculated in one non-limiting embodiment. $\begin{matrix} {\delta_{SD} = {{{K_{SD}^{o}\left( V_{x} \right)} \cdot {\overset{.}{V}}_{y}} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{SD}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{SD}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{SD}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot {\overset{.}{V}}_{y}}}} & (4) \end{matrix}$ where,

K⁰ _(SD)(V_(x)) is the nominal side-slip rate feedback gain table as a function of the vehicle speed; and ${{{{{\frac{\Delta\quad K_{SD}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{SD}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{SD}}{\Delta\quad D_{R}}}}_{o}$ is the side-slip rate gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.

FIGS. 6(a) and 6(b) are graphs with vehicle speed on the horizontal axis and side-slip rate feedback angle on the vertical axis showing examples of gain sensitivities corresponding to changes in the front cornering compliance and the rear cornering compliance, respectively.

The adapted yaw rate feedback angle signal δ_(RP), the adapted yaw acceleration feedback angle signal δ_(RD), the adapted side-slip feedback angle signal δ_(SP) and the adapted side-slip rate feedback angle signal δ_(SD) are added together by adders 130, 132 and 134 to generate the closed-loop feedback signal δ_(CL). If the switch 92 is closed, the closed-loop feedback signal δ_(CL) is added to the open-loop steering signal δ_(OL) by an adder 136 to generate the front-wheel steering angle signal δ_(F) that is applied to the actuator 32.

The foregoing discussion discloses and describes merely exemplary embodiments of the present invention. One skilled in the art will readily recognize from such discussion and from the accompanying drawings and claims that various changes, modifications and variations can be made therein without departing from the spirit and scope of the invention as defined in the following claims. 

1. Closed-loop control system providing a steering control signal for front wheels of a vehicle, said system comprising: a vehicle dynamics parameter estimation sub-system providing difference signals indicative of change between estimated and nominal vehicle dynamics parameters; a closed-loop adaptive compensation sub-system providing at least one of nominal yaw rate, yaw acceleration signal, side-slip signal and side-slip rate signals, and respective corresponding at least one of corrected yaw rate, yaw acceleration, side-slip and side-slip rate signals; and said steering control signal based on said at least one of said nominal signals and said respective corresponding at least one of said corrected signals.
 2. Control system for providing active front-wheel steering for a vehicle, said system comprising: a vehicle dynamics parameter estimation sub-system responsive to input signals, said vehicle dynamics parameter estimation sub-system employing a parameter estimation algorithm for estimating vehicle parameters based on the input signals, said vehicle dynamics parameter estimation sub-system comparing the estimated vehicle parameters with nominal vehicle parameters and generating difference signals indicative of the change between the estimated vehicle dynamics parameters and the nominal vehicle dynamics parameters; and a closed-loop control sub-system being responsive to the vehicle speed signal and the input signals applied to the vehicle dynamics parameter estimation sub-system for generating a closed-loop steering control signal to the front wheels of the vehicle, said closed-loop control sub-system including at least one look-up table providing a nominal closed-loop steering angle signal and at least one closed-loop adaptive compensation sub-system providing a corrected closed-loop steering angle signal, said closed-loop steering control signal comprising a combination of the nominal closed-loop steering angle signal and the corrected closed-loop steering angle signal.
 3. The system according to claim 2 wherein the at least one closed-loop look-up table and the at least one closed-loop adaptive compensation sub-system include a yaw rate feedback look-up table and a yaw rate feedback adaptive compensation sub-system, said yaw rate feedback look-up table providing an original yaw rate feedback angle signal and said yaw rate feedback adaptive compensation sub-system providing a corrected yaw rate feedback angle signal based on the estimated vehicle dynamics parameters.
 4. The system according to claim 3 wherein the yaw rate feedback adaptive compensation sub-system generates the corrected yaw rate feedback angle signal in accordance with the relationship: $\delta_{RP} = {{{K_{RP}^{o}\left( V_{x} \right)} \cdot \left( {\Omega_{c} - \Omega} \right)} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{RP}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{RP}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{RP}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot \left( {\Omega_{c} - \Omega} \right)}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; K⁰ _(RP) (V_(x)) is the nominal yaw rate feedback gain table as a function of vehicle speed; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; and ${{{{{\frac{\Delta\quad K_{RP}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{RP}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{RP}}{\Delta\quad D_{R}}}}_{o}$ is the yaw rate P-gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 5. The system according to claim 2 wherein the at least one closed-loop look-up table and the at least one closed-loop adaptive compensation sub-system include a yaw acceleration feedback look-up table and a yaw acceleration feedback adaptive compensation sub-system, said yaw acceleration feedback look-up table providing an original yaw acceleration feedback angle signal and said yaw acceleration feedback adaptive compensation sub-system providing a corrected yaw acceleration feedback angle signal based on the estimated vehicle dynamics parameters.
 6. The system according to claim 5 wherein the yaw acceleration feedback compensation sub-system generates the corrected yaw acceleration feedback angle in accordance with the relationship: $\delta_{RD} = {{{K_{RD}^{o}\left( V_{x} \right)} \cdot \left( {{\overset{.}{\Omega}}_{c} - \overset{.}{\Omega}} \right)} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{RD}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{RD}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{RD}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot \left( {{\overset{.}{\Omega}}_{c} - \overset{.}{\Omega}} \right)}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; K⁰ _(RD)(V_(x)) is the nominal yaw acceleration feedback gain table as a function of the vehicle speed; and ${{{{{\frac{\Delta\quad K_{RD}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{RD}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{RD}}{\Delta\quad D_{R}}}}_{o}$ is the yaw acceleration D-gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 7. The system according to claim 2 wherein the at least one closed-loop look-up table and the at least one closed-loop adaptive compensation sub-system include a side-slip feedback look-up table and a side-slip feedback adaptive compensation sub-system, said side-slip feedback look-up table providing an original side-slip feedback angle signal and said side-slip feedback adaptive compensation sub-system providing a corrected side-slip feedback angle signal based on the estimated vehicle dynamics parameters.
 8. The system according to claim 7 wherein the side-slip feedback adaptive compensation sub-system generates the corrected side-slip feedback angle signal in accordance with the relationship: $\delta_{SP} = {{{K_{SP}^{o}\left( V_{x} \right)} \cdot V_{y}} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{SP}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{SP}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{SP}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot V_{y}}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; K⁰ _(SP)(V_(x)) is the nominal side-slip feedback gain table as a function of the vehicle speed; and ${{{{{\frac{\Delta\quad K_{SP}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{SP}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{SP}}{\Delta\quad D_{R}}}}_{o}$ is the side-slip gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 9. The system according to claim 2 wherein the at least one closed-loop look-up table and the at least one closed-loop adaptive compensation sub-system include a side-slip rate feedback look-up table and a side-slip rate feedback adaptive compensation sub-system, said side-slip rate feedback look-up table providing an original side-slip rate feedback angle signal and said side-slip rate feedback adaptive compensation sub-system providing a corrected side-slip rate feedback angle signal based on the estimated vehicle dynamics parameters.
 10. The system according to claim 9 wherein the side-slip rate feedback adaptive compensation sub-system generates the corrected side-slip rate feedback angle in accordance with the relationship: $\delta_{SD} = {{{K_{SD}^{o}\left( V_{x} \right)} \cdot {\overset{.}{V}}_{y}} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{SD}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{SD}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{SD}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot {\overset{.}{V}}_{y}}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; K⁰ _(SD)(V_(x)) is the nominal side-slip rate feedback gain table as a function of the vehicle speed; and ${{{{{\frac{\Delta\quad K_{SD}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{SD}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{SD}}{\Delta\quad D_{R}}}}_{o}$ is the side-slip rate gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 11. The system according to claim 2 wherein the vehicle dynamics parameter estimation sub-system receives a steering wheel angle signal, a vehicle lateral acceleration signal, a vehicle yaw rate signal and the vehicle speed signal as the input signals.
 12. Control system for providing active front-wheel steering for a vehicle, said system comprising: a vehicle dynamics parameter estimation sub-system responsive to input signals including a front-wheel steering angle signal, a vehicle lateral acceleration signal, a vehicle yaw rate signal and the vehicle speed signal, said vehicle dynamics parameter estimation sub-system employing a linear parameter estimation algorithm for estimating vehicle parameters based on the input signals, said vehicle dynamics parameter estimation system comparing the estimated vehicle parameters with nominal vehicle parameters and generating difference signals indicative of the change between the estimated vehicle dynamics parameters and the nominal vehicle dynamic parameters; and a closed-loop control sub-system being responsive to the vehicle speed signal and the input signals applied to the vehicle dynamics parameter estimation sub-system for generating a closed-loop steering control signal to the front wheels of the vehicle, said closed-loop sub-system including include a yaw rate feedback look-up table and a yaw rate feedback adaptive compensation sub-system, said yaw rate feedback look-up table providing an original yaw rate feedback angle signal and said yaw rate feedback adaptive compensation sub-system providing a corrected yaw rate feedback angle signal based on the estimated vehicle dynamics parameters, said closed-loop sub-system further including a yaw acceleration feedback look-up table and a yaw acceleration feedback adaptive compensation sub-system, said yaw acceleration feedback look-up table providing an original yaw acceleration feedback angle signal and said yaw acceleration feedback adaptive compensation sub-system providing a corrected yaw acceleration feedback angle signal based on the estimated vehicle dynamics parameters, said closed-loop sub-system further including a side-slip feedback look-up table and a side-slip feedback adaptive compensation sub-system, said side-slip feedback look-up table providing an original side-slip feedback angle signal and said side-slip feedback adaptive compensation sub-system providing a corrected side-slip feedback angle signal based on the estimated vehicle dynamics parameters and said closed-loop sub-system further including a side-slip rate feedback look-up table and a side-slip rate feedback adaptive compensation sub-system, said side-slip rate feedback look-up table providing an original side-slip rate feedback angle signal and said side-slip rate feedback adaptive compensation sub-system providing a corrected side-slip rate feedback angle signal based on the estimated vehicle dynamics parameters, wherein said closed-loop steering control signal comprises the original yaw rate feedback angle signal, the corrected yaw rate feedback angle signal, the original yaw acceleration feedback angle signal, the corrected yaw acceleration feedback angle signal, the original side-slip feedback angle signal, the corrected side-slip feedback angle signal and the original side-slip rate feedback angle signal.
 13. Method for providing active front-wheel steering for a vehicle, said method comprising: receiving vehicle input signals, including vehicle speed; estimating vehicle parameters based on the input signals, comparing the estimated vehicle parameters with nominal vehicle parameters and generating difference signals indicative of the change between the estimated vehicle dynamics parameters and the nominal vehicle dynamic parameters; and generating a nominal closed-loop steering angle signal based on the input signals and the nominal vehicle parameters; generating a corrected closed-loop steering angle signal based on the vehicle input signals and the difference signals; and generating a closed-loop steering angle control signal to the front wheels of the vehicle based on the nominal closed-loop steering angle signal and the corrected closed-loop steering angle signal.
 14. The method according to claim 13 wherein generating the nominal closed-loop steering angle signal includes generating an original yaw rate feedback angle signal and wherein generating the corrected closed-loop steering angle signal includes generating a corrected yaw rate feedback angle signal in accordance with the relationship: $\delta_{RP} = {{{K_{RP}^{o}\left( V_{x} \right)} \cdot \left( {\Omega_{c} - \Omega} \right)} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{RP}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{RP}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{RP}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot \left( {\Omega_{c}\quad - \quad\Omega} \right)}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; K⁰ _(RP)(V_(x)) is the nominal yaw rate feedback gain table as a function of vehicle speed; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; and ${{{{{\frac{\Delta\quad K_{RP}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{RP}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{RP}}{\Delta\quad D_{R}}}}_{o}$ is the yaw rate P-gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 15. The method according to claim 13 wherein generating the nominal closed-loop steering angle signal includes generating an original yaw acceleration feedback angle signal and wherein generating the corrected closed-loop steering angle signal includes generating a corrected yaw acceleration feedback angle signal in accordance with the relationship: $\delta_{RD} = {{{K_{RD}^{o}\left( V_{x} \right)} \cdot \quad\left( {{\overset{\quad.}{\Omega}}_{c} - \overset{\quad.}{\Omega}}\quad \right)} + {\begin{pmatrix} {{{\frac{\Delta\quad K_{RD}}{{\Delta\quad T}\quad}}_{o}\quad\Delta\quad{T\left( V_{x} \right)}} +} \\ {{{\frac{\Delta\quad K_{RD}}{\Delta\quad D_{F}}}_{o}\quad\Delta\quad D_{F}} +} \\ {{\frac{\Delta\quad K_{RD}}{\Delta\quad D_{R}}}_{o}\quad\Delta\quad D_{R}} \end{pmatrix} \cdot \left( {{\overset{\quad.}{\Omega}}_{c} - \overset{\quad.}{\Omega}}\quad \right)}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; K⁰ _(RD)(V_(x)) is the nominal yaw acceleration feedback gain table as a function of the vehicle speed; and ${{{{{\frac{\Delta\quad K_{RD}}{{\Delta\quad T}\quad}}_{o},\frac{\Delta\quad K_{RD}}{\Delta\quad D_{F}}}}_{o};\frac{\Delta\quad K_{RD}}{\Delta\quad D_{R}}}}_{o}$ is the yaw acceleration D-gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 16. The method according to claim 13 wherein generating the nominal closed-loop steering angle signal includes generating an original side-slip feedback angle signal and wherein generating the corrected closed-loop steering angle signal includes generating a corrected side-slip feedback angle signal in accordance with the relationship: $\delta_{SP} = {{{K_{SP}^{o}\left( V_{x} \right)} \cdot V_{y}} + {\left( \frac{\Delta\quad K_{SP}}{\Delta\quad T} \middle| {}_{o}{{\Delta\quad{T\left( V_{x} \right)}} + \frac{\Delta\quad K_{SP}}{\Delta\quad D_{F}}} \middle| {}_{o}{{\Delta\quad D_{F}} + \frac{\Delta\quad K_{SP}}{\Delta\quad D_{R}}} \middle| {}_{o}{\Delta\quad D_{R}} \right) \cdot V_{y}}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; K⁰ _(SP)(V_(x)) is the nominal side-slip feedback gain table as a function of the vehicle speed; and $\left. \frac{\Delta\quad K_{SP}}{\Delta\quad T} \right|_{o},{\left. \frac{\Delta\quad K_{SP}}{\Delta\quad D_{F}} \right|_{o};\left. \frac{\Delta\quad K_{SP}}{\Delta\quad D_{R}} \right|_{o}}$ is the side-slip gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 17. The method according to claim 13 wherein generating the nominal closed-loop steering angle signal includes generating an original side-slip rate feedback angle signal and wherein generating the corrected closed-loop steering angle signal includes generating a corrected side-slip rate feedback angle signal in accordance with the relationship: $\delta_{SD} = {{{K_{SD}^{o}\left( V_{x} \right)} \cdot V_{y}} + {\left( \frac{\Delta\quad K_{SD}}{\Delta\quad T} \middle| {}_{o}{{\Delta\quad{T\left( V_{x} \right)}} + \frac{\Delta\quad K_{SD}}{\Delta\quad D_{F}}} \middle| {}_{o}{{\Delta\quad D_{F}} + \frac{\Delta\quad K_{SD}}{\Delta\quad D_{R}}} \middle| {}_{o}{\Delta\quad D_{R}} \right) \cdot V_{y}}}$ where, Ω is the yaw rate; Ω_(c) is the yaw rate command; ΔD_(F) is the change in the front cornering compliance; ΔD_(R) is the change in the rear cornering compliance; ΔT is the deviation in the open-loop gain; K⁰ _(SD)(V_(x)) is the nominal side-slip rate feedback gain table as a function of the vehicle speed; and $\left. \frac{\Delta\quad K_{SD}}{\Delta\quad T} \right|_{o},{\left. \frac{\Delta\quad K_{SD}}{\Delta\quad D_{F}} \right|_{o};\left. \frac{\Delta\quad K_{SD}}{\Delta\quad D_{R}} \right|_{o}}$ is the side-slip rate gain sensitivity to open-loop gain, front cornering compliance, and rear cornering compliance, respectively.
 18. The method according to claim 13 wherein receiving the vehicle input signals includes receiving a steering wheel angle signal, a vehicle lateral acceleration signal, a vehicle yaw rate signal and the vehicle speed signal as the input signals. 